structure of certain banach algebra products

Structure of Certain Banach Algebra Products

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.

The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra B(E) of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and `p for 1 6 p < ∞. We add a new member to this family by showing that there are exactly four closed ideals in B(E) for t...

On the Arens Products and Certain Banach Algebras

In this paper, we study several problems in Banach algebras concerned with the Arens products.

Topological Centers of Certain Banach Module Actions

Homomorphism Weak amenability of certain Banach algebras

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra